Explore BrainMass

# Real Analysis Topology and Sigma-Algebra

Not what you're looking for? Search our solutions OR ask your own Custom question.

This content was COPIED from BrainMass.com - View the original, and get the already-completed solution here!

1). Prove that any sigma-algebra, which contains a finite number of members is also a topology. ( The Q in another words : to show that there exist a sequence of disjoint members of a sigma algebra which contains infinite no. of members).

2). Does there exist an infinite sigma-algebra which has only countably many members? (Of course justify, examples, anything needed to prove any claims made in the solution.)

https://brainmass.com/math/real-analysis/real-analysis-topology-sigma-algebra-48330

#### Solution Preview

1. Proof:
We check the definition of sigma-algebra of topology. Suppose F is a sigma-algebra defined on the set X. We want to show that F is also a ...

#### Solution Summary

Sigma-algebras are investigated. The solution is detailed and well presented.

\$2.49